Stress and deformation analysis of the steel pipe arch integral lifting construction process of a continuous beam arch bridge

The Changjinghuang Railway Xinjiang Xizhi Bridge is a (90 + 180 + 90) m continuous beam arch bridge, and the arch rib steel pipe installation adopts “short bracket assembly and overall lifting method”. In order to ensure the accuracy of closure, the stress and deformation of the arch rib and bracket must be strictly controlled. Midas Civil is used to establish the finite element model to simulate the overall lifting construction process of the arch rib. Based on the model, the stress and deformation of the arch rib and the supports are analyzed, and the determination method of the horizontal cable force under temperature variations is proposed. The results show that the stress and deformation of the arch rib and bracket meet the requirements. Considering the variation of temperature, the tension force of the horizontal cables is taken as 200 t. The construction plan proposed under the guidance of numerical calculation results has been proven by practical engineering to meet the requirement of closure accuracy, which can be used as a reference for similar projects.

www.nature.com/scientificreports/Zizilu Bridge in Longxing New Town of Chongqing Liangjiang New District adopts the bracket method and vertical lifting method to carry out the construction of the arch rib, and the maximum closing error is 22.7 mm, meeting the design requirements 17 .In the construction of large-span arch bridges, the overall lifting method is usually used in conjunction with the bracket method.The arch ribs are assembled on the short bracket first and then lifted to the designated position.The existing engineering practice shows that the short bracket assembly and overall lifting method not only has the characteristics of simple operation and high safety of the bracket method, but also has the advantages of short construction period and less high altitude operation of the overall lifting method 18 .However, due to the strong dependence of the overall lifting construction method on lifting facilities, the overall lifting method started late, and engineering applications are not as rich as other methods 19 .Therefore, there are many problems that need to be solved during the construction process, such as the stability of the brackets and the deformation of the arch ribs.
Based on the development status and characteristics of the short bracket assembly and overall lifting method, this paper establishes a finite element model according to the construction plan of the Changjinghuang Railway Xinjiang Xizhi Bridge.Based on the established model, the stress and deformation of the arch rib and the supports are analyzed, and the determination method of the horizontal cable force under temperature variations is proposed.A detailed construction plan is put forward with the numerical calculation results as a guide.

Project background
The main bridge of the Changjinghuang Railway Xinjiang Bridge adopts (90 + 180 + 90) m prestressed concrete continuous girder arch structure.The schematic diagram of the bridge structure is shown in Fig. 1.
The main girder adopts a single-box double-compartment prestressed concrete box-type variable crosssection with a deck width of 13.2 m and a mid-span height of 5.0 m.The arch rib adopts vertical parallel steel pipe concrete dumbbell arch, with the arch axis adopting a quadratic parabolic line.The center distance between the two arch ribs is 11.9 m, the calculated span is 180 m, and the vector height of the arch rib elevation is 36 m.There are nine cross braces between two bays of arch ribs, and the cross braces are space truss braces.Each cross brace is composed of four main steel pipes of φ500 × 14 mm and 32 connecting steel pipes of φ250 × 10 mm.The distance between the suspenders along the bridge direction is 9 m, and there are 18 sets of double suspenders in the entire bridge.The upper end of the boom passes through the arch rib and is anchored to the tension base at the upper edge of the arch rib, while the lower end is anchored to the fixed base at the lower edge of the crossbeam at the suspension point.
The arch rib steel pipe installation adopts "short bracket assembly and overall lifting method".The highest bracket is 17 m, and the lowest is 6.6 m.The embedded parts on the main beam are welded to the bottom of the bracket to ensure the accuracy of the support position.The arch rib assembly bracket is made of φ273 × 8 steel pipe, and the scissors support is made of〔12 a channel steel.The distribution beam at the top of the column is made of 32 a I-beam, and the web plate is welded with stiffeners corresponding to the stress-bearing position.The column of the overall lifting frame of the arch rib is made of φ426 × 8 steel pipe, and the diagonal bracing at the cantilever end of the distribution beam is made of φ273 × 12 steel pipe.

Numerical model
Figure 2 shows the finite element model established, which mainly consists of arch ribs, assembly supports, overall lifting supports, cross braces, horizontal tie rods, and vertical lifting cables.Table 1 shows the relevant material parameters.
The height of the lifting bracket is 28.5 m, the maximum height of the assembly bracket is 17 m, and the minimum is 6 m.The length of the lifting section of the arch rib is 112.4 m and the lifting height is 17.76 m.The arch ribs, cross braces, and supports are simulated by beam units, and the horizontal tie rods and vertical lifting cables are simulated by tension-only truss units.The tension force of the horizontal ties rods and the lifting force of the vertical lifting cables are applied by initial tension loads.
The bottom of the supports is fixed and restrained.The constraints between the assembly support, and the arch ribs are simulated by 'Rigid connection' in the low-level assembly stage, while 'Only-compression elastic connection' in the trial lifting stage.The constraints between arch ribs and cross braces are simulated by 'Elastic connection' .The connections between the arch rib and horizontal tie rods, as well as the vertical lifting cables, www.nature.com/scientificreports/all adopt a 'Rigid connection' .The 'Rigid connections' are used to simulate the constraints between the vertical lifting cables and the distribution beams at the top of the overall lifting supports 20 .
Arch ribs and supports are mainly subjected to self-weight loads and wind loads.The self-weight load is automatically calculated by Midas Civil software, and the wind load is calculated by the following formula 21 : where W : is the wind strength (Pa), K 1 : is the shape coefficient of wind load, K 2 : is the coefficient of wind pressure variation with height, K 3 : is the geographical coefficient, W 0 : is the basic wind strength (Pa).
After calculation, the wind strength of the arch rib is taken as 753.5 Pa, and the wind strength of the supports is taken as 548 Pa.
Three construction stages, including low-level assembly, trial lifting, and formal lifting, are selected for modeling analysis to analyse the stress and deformation of the structure during the construction process.The calculation models of the three construction stages are shown in Figs. 3, 4, 5.

Force analysis of the supports
The self-weight load of the arch rib is borne by the assembly supports in the low-level assembly stage, which is the most unfavorable working condition of the assembly supports.Therefore, the low-level assembly stage is chosen to analyze the stability of the assembly supports.The stress and deformation of the assembly support in the low-level assembly stage are shown in Fig. 7.
According to the standard for design of steel structures, the design value of compressive strength of Q235 steel f d is 215 MPa, and the design value of shear strength f v is 125 MPa 22 .As shown in Fig. 6, the maximum stress  www.nature.com/scientificreports/ of the assembly supports is σ max = 167 MPa < f d = 215 MPa and the maximum shearing stress of the assembly ssupportsσ max = 9.8 MPa < f v = 125 MPa , which means that the strength of the assembly supports meets the design requirements.In the low-level assembly stage, both of the maximum stress and maximum shearing stress appear at the outermost assembly supports of the lifting section.
The steel structure is permitted to deflect up to 1/400 of its span length under the constant and live loads 22 .The allowable deflection of the supporting beams on the top of the assembly supports is 1000/400 = 2.5 mm, and the allowable value of horizontal displacement at the top of the support is 16,600/400 = 41.5 mm.It can be seen from Fig. 6 that the maximum vertical displacement of the assembly supports is 1 mm, appearing at the supporting beam, and the maximum horizontal displacement of the assembly supports is 18 mm, appearing at the top of the middle assembly supports of the lifting section.Therefore, the stiffness of the assembly supports meets the design requirements.
The self-weight load of the arch rib in the formal lifting stage is borne by the overall lifting supports, which is the most unfavorable working condition of the overall lifting supports.Therefore, the overall lifting stage is chosen to analyse the stability of the lifting supports.The stress and deformation of the overall lifting supports in the low-level assembly stage are shown in Fig. 7.
As shown in Fig. 7, the maximum stress of the overall lifting supports is σ max = 116 MPa < f d = 215 MPa and the maximum shearing stress of the overall lifting spports is σ max = 64MPa < f v = 125 MPa , which means that the strength of the overall lifting supports meets the design requirements.In the formal lifting stage, the maximum stress appears at the bottom of the overall lifting supports, and the maximum shearing stress appears at the supporting beam on the top of the overall lifting supports.
The allowable deflection of the supporting beams on the top of the overall lifting supports is 2000/400 = 5 mm, and the allowable value of horizontal displacement at the top of the support is 28,000/400 = 70 mm.It can be seen from Fig. 7, the maximum vertical displacement of the overall lifting supports is 3.7 mm appearing at the supporting beam, and the maximum horizontal displacement of the overall lifting supports is 11 mm appearing at the top of the overall lifting supports.Therefore, the stiffness of the overall lifting supports meets the design requirements.During the integral lifting of the arch rib, horizontal tie rods are arranged at both ends of each arch rib to constrain the horizontal deformation of the ends.Meanwhile, vertical lifting cables are installed at both ends of each arch rib to provide vertical support for the arch rib.Therefore, the overall stress state of the arch rib during the integral lifting process is that the arch rib forms a self-balancing state under the combined action of the selfweight, the horizontal tensile force, and the vertical lifting force.By applying accurate horizontal tension cable forces and adopting reasonable construction measures and monitoring methods, the control requirements for the integral lifting of the arch rib can be achieved.To obtain the reasonable cable force, the following methods are employed in the formal lifting calculation model: ① Set the stiffness of the horizontal cables in the formal lifting calculation model to infinite, so that the cables are passively stressed, and run the model to obtain the initial cable force Ti. www.nature.com/scientificreports/② Fine-tune the initial cable force Ti to make the horizontal displacement at both ends of the arch rib as close to 0 as possible, and obtain the optimal cable force To. ③ Change the temperature, repeat the above steps, and obtain the optimal cable force To under each temperature condition.
After calculation, the initial cable force value Ti was determined to be 190.05 t, with a horizontal displacement of 0.54 mm at both ends of the arch rib.After continuous adjustments, the optimal cable force value T0 reached 190.73 t, resulting in a horizontal displacement of 0.01 mm at both ends of the arch rib.We then calculated the optimal cable force for temperature variations ranging from ΔT = − 10-10 °C and performed a linear fitting.The results are presented in Fig. 9.It can be seen from the results presented in Fig. 9 that the optimal horizontal cable force is linearly correlated with the overall temperature of the arch rib.Considering the temperature of the construction site, the tension force of the horizontal tie is taken as 200 t.

Force and deformation analysis of the lifting process
The self-weight of the lifting section of the arch rib is about 440 t, and the tension force of the horizontal tie rods is 200 t.Due to the large lifting weight and tension force, the horizontal force and lifting force should be loaded in a graded and synchronized manner to keep the stress and deformation of the arch rib and brackets under control.As shown in Table 2, the tension in the horizontal and vertical cables is increased by 25% of the target cable force each time until the arch ribs detach from the supports, corresponding to CS1 to CS5, respectively.The trial lifting loading process is divided into five working conditions, and the specific loading conditions are shown in Table 2.
Figure 10 shows the deformation and stress of the arch rib after the tension force is applied in each stage of CS1-CS5.In CS1-CS3, as the load increases, the maximum stress of the arch rib increases linearly, while the vertical elongation deformation and horizontal shrinkage deformation of the arch rib do not change much.This  www.nature.com/scientificreports/ is because the arch ribs in CS1-CS3 have not been completely detached, which leads to a certain supporting effect on the arch ribs, so the deformation and stress of the arch ribs are more reasonable.In CS3-CS4, the horizontal deformation and vertical deformation of the arch rib increase greatly because the middle part of the arch rib is decoupled from the supports when the horizontal force and vertical force reach the target value.In CS4-CS5, due to the detachment of the arch ribs, the vault is deflected downward by its own weight, so the vertical deformation of the arch ribs changes from elongation deformation to shrinkage deformation, and the horizontal deformation of the arch ribs is on the contrary.Although CS5 has larger deformation and stress than the previous four loading conditions, the mechanical performance of the arch rib structure during the lifting process is still good, which can meet the design and construction requirements.

Short bracket assembly and overall lifting method
The construction process of short bracket assembly and the overall lifting method is as follows: supports installation → low-level assembly → trial lifting → formal lifting → arch rib closing

Supports installation
The assembly supports are installed from the arch foot to the middle of the span, and the specific construction steps are as follows: reviewing the position of the pre-embedded parts → assembling the pipe piles on site → assembling the connection system → installing the lattice columns → installing the transverse distributing beams → inspecting and checking the acceptance.The distribution beam on the top of the column adopts 40 a I-beam, and the I-beam web plate is welded with stiffening ribs corresponding to the stress position.The top of the distribution beam adopts a steel pipe short pier as the elevation adjustment pier, and the angle is set according to the arch axis line type and welded on the distribution beam.To maintain the lateral stability of assembly supports, pre-embedded parts are welded with steel pipes at the bottom of the support.When the support exceeds 12 m, wind cables are installed.The top of the wind cables is connected to the top of the support, and the bottom is connected to the pre-embedded reinforcement on the beam surface.After the bracket installation is completed, the welds and connections of the bracket are checked, and the position of the arch rib positioning saddle is adjusted so that the axis and elevation of the positioning saddle meet the installation requirements.

Low-level assembly
There are 4 small segments in the arch rib of the non-lifting section, and the weight of a single piece is about 20.6 t.They are all installed separately with 80t truck cranes, and the lifting height is 13.5 m.The next construction section can only be carried out after the temporary plate is firmly welded.After the left and right arch rib segments on one side are installed, hoist and install the cross braces in time and weld them firmly with the arch

Figure 4 .
Figure 4. Calculation model of trial lifting.

Figure 5 .
Figure 5. Calculation model of formal lifting.

Figure 9 .
Figure 9. Optimal cable force in different temperature.

Table 1 .
Parameters of the superstructure and temporary support system.

Table 2 .
Trial lifting stage loading conditions.